Ez.eqn9.supp {calibrator} R Documentation

## Expectation as per equation 10 of KOH2001

### Description

Expectation as per equation 10 of KOH2001 (not the supplement)

### Usage

Ez.eqn9.supp(x, theta, d, D1, D2, H1, H2,  phi)
Ez.eqn9.supp.vector(x, theta, d, D1, D2, H1, H2, phi)


### Arguments

 x point at which expectation is needed theta parameters d observations and code outputs D1 code run points D2 observation points H1 regression function for D1 H2 regression function for D2 phi hyperparameters

### Details

The user should always use Ez.eqn9.supp(), which is a wrapper for Ez.eqn9.supp.vector(). The forms differ in their treatment of \theta. In the former, \theta must be a vector; in the latter, \theta may be a matrix, in which case Ez.eqn9.supp.vector() is applied to the rows.

Note that Ez.eqn9.supp.vector() is vectorized in x but not \theta (if given a multi-row object, apply(theta,1,...) is used to evaluate the function for each row supplied).

Function Ez.eqn9.supp() will take multiple-row arguments for x and theta. The output will be a matrix, with rows corresponding to the rows of x and columns corresponding to the rows of theta. See the third example below.

Note that function Ez.eqn9.supp() determines whether there are multiple values of \theta by is.vector(theta). If this returns TRUE, it is assumed that \theta is a single point in multidimensional parameter space; if FALSE, it is assumed to be a matrix whose rows correspond to points in parameter space.

So if \theta is one dimensional, calling Ez.eqn9.supp() with a vector-valued \theta will fail because the function will assume that \theta is a single, multidimensional, point. To get round this, use as.matrix(theta), which is not a vector; the rows are the (1D) parameter values.

### Author(s)

Robin K. S. Hankin

### References

• M. C. Kennedy and A. O'Hagan 2001. Bayesian calibration of computer models. Journal of the Royal Statistical Society B, 63(3) pp425-464

• M. C. Kennedy and A. O'Hagan 2001. Supplementary details on Bayesian calibration of computer models, Internal report, University of Sheffield. Available at http://www.tonyohagan.co.uk/academic/ps/calsup.ps

• R. K. S. Hankin 2005. Introducing BACCO, an R bundle for Bayesian analysis of computer code output, Journal of Statistical Software, 14(16)

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### Examples

data(toys)
Ez.eqn9.supp(x=x.toy,  theta=theta.toy, d=d.toy, D1=D1.toy,
D2=D2.toy, H1=H1.toy,H2=H2.toy, phi=phi.toy)

Ez.eqn9.supp(x=D2.toy, theta=t.vec.toy,  d=d.toy, D1=D1.toy,
D2=D2.toy, H1=H1.toy,H2=H2.toy, phi=phi.toy)

Ez.eqn9.supp(x=x.vec,  theta=t.vec.toy,  d=d.toy, D1=D1.toy,
D2=D2.toy, H1=H1.toy,H2=H2.toy, phi=phi.toy)



[Package calibrator version 1.2-8 Index]